What is the Least Common Multiple of 20304 and 20308?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 20304 and 20308 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20304 and 20308, than apply into the LCM equation.

GCF(20304,20308) = 4
LCM(20304,20308) = ( 20304 × 20308) / 4
LCM(20304,20308) = 412333632 / 4
LCM(20304,20308) = 103083408

Least Common Multiple (LCM) of 20304 and 20308 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20304 and 20308. First we will calculate the prime factors of 20304 and 20308.

Prime Factorization of 20304

Prime Factorization of 20308

Now multiplying the highest exponent prime factors to calculate the LCM of 20304 and 20308.

LCM(20304,20308) = 2⁴ × 3³ × 47¹ × 5077¹
LCM(20304,20308) = 103083408